He thinks because he works hard and makes a good living, that’s sufficient.

Having a job is generally good! However, it is not the same as actually being a parent. LW's husband is using his employment as an excuse to avoid parenting and gets angry when parenting obligations present themselves to him, such as when his children complain about seeing upsetting things in the media he watches. If he really wants to limit his parental obligations to his paycheck, then he can start by negotiating a particularly generous alimony arrangement with his soon-to-be ex-wife.